Final answer:
The correct option, in this case, is C) undefined. The limit of cos(x) as x approaches infinity is undefined because the cosine function oscillates between -1 and 1 and does not approach a single value.
Step-by-step explanation:
The question concerning the limit of cos(x) as x approaches infinity deals with a fundamental concept in trigonometry and calculus. The cosine function oscillates between -1 and 1 for all real numbers.
Therefore, as x approaches infinity, the cosine function does not settle towards any single value but continues to fluctuate. This behavior implies that the limit does not exist because there is no single value that cos(x) approaches as x becomes infinitely large.
Furthermore, it's important to note that the cosine function is periodic with a period of 2π radians (or 360 degrees), which means that it repeats its values over regular intervals. Due to this periodicity and the bound nature of the cosine function, it doesn't have an asymptote like some functions where they consistently approach a specific value at infinity. The correct option, in this case, is C) undefined.